The acidosis in DKA should resolve with adequate fluid and insulin therapy and we would usually not use bicarbonate. Acidosis can be regarded as an adaptive response which improves oxygen delivery by causing a right shift of the oxygen dissociation curve. Giving bicarbonate can cause a rise in the CO2 partial pressure in the cerebrospinal fluid (CSF) and as such to a paradoxical increase in CSF acidosis. Bicarbonate in DKA may delay the fall in blood lactate: pyruvate ratio and ketones and may as already mentioned by Jaikrit increase the risk of cerebral oedema - particular in children and young adults.
I disagree with the statement that "the blood bicarbonate concentration is usually not recommended to monitor the progress of treatment of DKA". Actually, an increase in venous bicarbonate by 3 mmol per hour is one of the goals that you are trying to achieve with your therapy, together with reduction of blood ketones by 0.5 mmol/l/hour and reduction in blood glucose by 3 mmol/L/hour.
To add to both answers, in DKA you should follow anion gap, which is a surrogate marker for your bicarb levels.
If your anion gap opens up again, it means that your patient is either not resuscitated enough (with IV fluids, preferably lactate ringer's) or didn't receive enough insulin.